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Lesson plan Grade 7 English Language Arts

Parts Per Billion at Pinder Gap: Explaining Small Numbers

A grade 7 ELA lesson in which students rank three ways of explaining parts per billion in a water report, then write their own definition, comparison, and example.

Objectives

  1. Students will identify definition, comparison, and example as tools for explaining a unit.
  2. Students will rank three explanations of the same unit and justify the ranking with evidence.
  3. Students will write a short explanation of parts per billion for a named audience.

Vocabulary

Key words: parts per billion, definition, comparison, audience, detect

Teacher overview

Every community water system mails customers a yearly water quality report, and parts per billion is the unit in it that readers have the most trouble picturing. The misconception worth planning for is that a big-sounding word means a big quantity, so students read "40 parts per billion" as a large amount of something in the glass, and a second and equally common error is the belief that any amount a laboratory can detect must be unsafe. This lesson uses a draft newsletter from the fictional Pinder Gap Water District and asks students to judge which of three explanations a general reader could actually follow, then to write their own using definition, comparison, and example.

Procedure

Hook (5 min): Write the phrase "40 parts per billion" on the board with no context and ask students to write one sentence saying whether that sounds like a lot. Take a quick show of hands for "a lot" and "a little" and record the count. Tell students the class will return to the tally at the end of the period.

Reading the draft newsletter (10 min): Distribute the Student Handout. Students read the draft aloud in pairs, then mark the sentence that defines the unit, the sentence that compares it to something familiar, and the sentence that gives an example from the town of Pinder Gap. Confirm that most pairs found three different sentences before moving on.

Ranking the three explanations (10 min): Direct students to the three explanations at the end of the handout, each written by a different fictional staff member. Students rank them from clearest to least clear and note the reason for the top choice. Ask three students with different rankings to defend their first choice using a specific word or phrase from the explanation rather than a general impression.

Mini-lesson on the three tools (8 min): Name the three moves explicitly: a definition says what the unit is, a comparison ties it to something the reader already knows, and an example shows it doing work in a real decision. Show that an explanation using only one of the three leaves a gap, and ask the class which tool the weakest of the three ranked explanations is missing.

Drafting (9 min): Students complete handout items 6 and 7, writing for a reader who is a neighbor with no science background. Circulate and check that the comparison is not simply copied from the newsletter.

Closure (3 min): Return to the opening tally. Ask for a second show of hands on whether 40 parts per billion sounds like a lot, and ask two students who changed their vote to name the sentence that changed it. If fewer than half the class can name a specific sentence, reteach the comparison move before the next writing task.

Parts Per Billion at Pinder Gap: Explaining Small Numbers — Grade 7 English Language Arts
Name: ____________________________ Date: ______________

Student Handout

Draft newsletter from the Pinder Gap Water District.

Once a year we mail every household a report on what is in the water. The report uses a unit called parts per billion, written ppb. A part per billion means one unit of a substance mixed into a billion units of water. It is a way to describe a very small share of a very large amount.

That is hard to picture, so try it this way. One part per billion is about one drop of food coloring in a tanker truck full of water. It is also about one second out of a stretch of time roughly thirty-two years long.

Small does not always mean harmless, and that is why the report exists. For lead, the action level is 15 ppb, and it drops to 10 ppb in 2027 under the federal Lead and Copper Rule Improvements. When the level in a system goes above the action level, the utility has to take specific steps. Our laboratory can measure amounts far below that level, so a number on the report is not a warning by itself. The number tells you where the water sits compared with the action level. EPA's health goal for lead is zero, so the action level is a signal for the utility to act, not a safe amount.

Three explanations of the same unit, written by three staff members.

Explanation A: Parts per billion, or ppb, is the unit we use for very small amounts. It is a ratio of one unit of a substance to one billion units of water.

Explanation B: Think of a tanker truck of water with one drop of food coloring in it. That is one part per billion. We use the unit because the amounts we look for are that small, and the action level for lead is 15 ppb, which is fifteen of those drops.

Explanation C: Parts per billion is a measure of concentration. Concentration expresses the quantity of a constituent relative to the total quantity of the mixture, expressed as a dimensionless ratio.

  1. According to the newsletter, what does one part per billion mean?
  2. Copy the sentence that gives a comparison you could picture.
  3. Copy the sentence that explains why a number on the report is not a warning by itself.
  4. According to the newsletter, what is the lead action level today, and what will it become in 2027?
  5. Rank the three explanations from clearest to least clear for a neighbor with no science background, and give one reason for your top choice.
  6. Write your own explanation of parts per billion in three sentences. Use a definition, then a comparison, then an example.
  7. Name the audience you wrote item 6 for, and name one word you chose because of that audience.
  8. Explanation C uses accurate words that most readers would not follow. Rewrite it in one sentence a seventh grader would understand.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: One unit of a substance mixed into a billion units of water.
    Accept wording such as one part in a billion parts. The point is the ratio, not the substance.
  2. Answer: Either the sentence about one drop of food coloring in a tanker truck or the sentence about one second in about thirty-two years.
    Both are comparisons, so accept either.
  3. Answer: The sentence saying the laboratory can measure amounts far below that level, so a number on the report is not a warning by itself.
    Accept the sentence copied in full or from "so" onward.
  4. Answer: 15 ppb today, and 10 ppb in 2027.
    Both figures come from the third paragraph of the newsletter.
  5. Answer: Accept any ranking defended with a specific word or phrase.
    Most students will rank B first because it gives a picture and a use. A student who ranks A first must point to its precision, and a student who ranks C first has to explain how a neighbor would follow "dimensionless ratio."
  6. Answer: Accept any three-sentence explanation with the three moves in order.
    Check that the comparison is the student's own and that the example names a decision, such as comparing a result with a limit.
  7. Answer: Accept any named audience with one word choice tied to it.
    A proficient answer names a real reader, such as a neighbor or a younger sibling, and explains the word choice, such as using "amount" instead of "concentration."
  8. Answer: Accept any accurate one-sentence rewrite in plain words.
    A strong rewrite keeps the idea that the unit compares the amount of one substance to the amount of everything it is mixed into, and drops "constituent" and "dimensionless."

Differentiation

Support

Give students the newsletter with the definition, comparison, and example sentences already boxed and labeled, so items 1 through 3 become a matter of reading the labels. Provide a three-line frame for item 6 with the sentence openers "Parts per billion means," "Picture," and "For example."

Extension

Ask students to write a fourth explanation aimed at a reader who is worried rather than curious, then annotate the draft to show which choices address the worry without hiding the number. Students can also compare their explanation with Explanation C and describe what accuracy costs when it is written that way.

ELL supports

Demonstrate the comparison with a clear jug of water and one drop of food coloring, and let students say what they see before they read. Pre-teach "ratio," "limit," and "detect" with cognates where they exist. Allow items 1 through 4 to be answered by highlighting the sentence in the text.

Extensions

Students find one unit from another subject that gives readers the same trouble, such as decibels or a percentage change, and write a three-sentence explanation using the same definition, comparison, and example structure. Post the explanations and have the class vote on which comparison would work best for a family member.